On MSRD Codes, h-Designs and Disjoint Maximum Scattered Linear Sets

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2025-01-29 DOI:10.1002/jcd.21972

Paolo Santonastaso, John Sheekey

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引用次数: 0

Abstract

In this paper, we construct new optimal subspace designs and, consequently, new optimal codes in the sum-rank metric. We construct new 1-designs by finding sets of disjoint maximum scattered linear sets, and use these constructions to also find new $h$ -designs for $h > 1$ . As a means of achieving this, we establish a correspondence between the metric properties of sum-rank metric codes and the geometric properties of subspace designs. Specifically, we determine the geometric counterpart of the coding-theoretic notion of generalised weights for the sum-rank metric in terms of subspace designs and determine a geometric characterisation of MSRD codes. This enables us to characterise subspace designs via their intersections with hyperplanes and via duality operations.

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关于MSRD规范、h-设计和不相交最大离散线性集

在本文中，我们构造了新的最优子空间设计，从而在和秩度量中构造了新的最优码。我们通过寻找不相交的最大分散线性集来构造新的1-设计，并利用这些构造来寻找h >的新的h -设计；1 .为了达到这个目的，我们建立了和秩度量码的度量性质与子空间设计的几何性质之间的对应关系。具体来说，我们在子空间设计方面确定了和秩度量的广义权重的编码理论概念的几何对应物，并确定了MSRD码的几何特征。这使我们能够通过它们与超平面的交点和对偶运算来表征子空间设计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Combinatorial Designs 数学-数学

CiteScore

1.60

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Combinatorial Designs is an international journal devoted to the timely publication of the most influential papers in the area of combinatorial design theory. All topics in design theory, and in which design theory has important applications, are covered, including: block designs, t-designs, pairwise balanced designs and group divisible designs Latin squares, quasigroups, and related algebras computational methods in design theory construction methods applications in computer science, experimental design theory, and coding theory graph decompositions, factorizations, and design-theoretic techniques in graph theory and extremal combinatorics finite geometry and its relation with design theory. algebraic aspects of design theory. Researchers and scientists can depend on the Journal of Combinatorial Designs for the most recent developments in this rapidly growing field, and to provide a forum for both theoretical research and applications. All papers appearing in the Journal of Combinatorial Designs are carefully peer refereed.